We can rewrite equations in standard form into slope-intercept form. Then, we can easily determine the slope and y𝑦-intercept of each equation.When graphing a straight line, two points on the line must be plotted and joined. If an equation is written in standard form, the x𝑥 and y𝑦-intercepts can be calculated and plotted on the Cartesian grid. These plotted points can then be joined to graph the line represented by the equation.Let’s look an example. ProblemGiven the equation 3x+2y=123𝑥+2𝑦=12 written in standard form, rewrite it in slope-intercept form. SolutionSlope-Intercept Form is in y= form, so we must solve the equation for y. First, subtract 3x3𝑥 from both sides of the equation to isolate the y𝑦 term.3x−3x+2y=12−3x3𝑥−3𝑥+2𝑦=12−3𝑥Next, simplify both sides of the equation.2y=12−3x2𝑦=12−3𝑥Next, rewrite the right side of the equation to correspond to y=mx+b𝑦=𝑚𝑥+𝑏. Remember that the Commutative Property of algebra tells us it’s ok to re-order the terms in an equation, and that a+b𝑎+𝑏 is the same as saying b+a𝑏+𝑎.2y=12−3x2𝑦=12−3𝑥2y=−3x+122𝑦=−3𝑥+12Then, divide both sides of the equation by 22 to solve for the variable y𝑦.2y2=−3x+1222𝑦2=−3𝑥+122y=−32x+𝑦=−32𝑥+ The slope of this line is and the y𝑦-intercept is at (0,(0, )).

To write an equation in slope-intercept form when given the slope and a point, you will need to follow several steps.Step 1: Begin by writing the formula for slope-intercept form: y=mx+b𝑦=𝑚𝑥+𝑏.Step 2: Substitute the given slope for m𝑚.Step 3: Use the ordered pair you are given (x,y)(𝑥,𝑦) and substitute these values for the variables x𝑥 and y𝑦 in the equation.Step 4: Solve for b𝑏 (the y𝑦-intercept of the graph).Step 5: Rewrite the original equation in Step 1, substituting the slope for m𝑚 and the y𝑦-intercept for b𝑏.First, determine what information is given. The value of the slope (m𝑚) is 33 and the line passes through the point (9,6)(9,6) which are the coordinates of a point (x,y)(𝑥,𝑦) on the line. We will work through the steps above with this specific problem.Step 1: Write the slope-intercept form for the equation of a line.y=mx+b𝑦=𝑚𝑥+𝑏Step 2: Fill the value for m𝑚 into the equation.y=𝑦= x+b𝑥+𝑏Step 3: Since the value of the y𝑦-intercept (b𝑏) is not known, use the coordinates (x=9,y=6)(𝑥=9,𝑦=6) of the point to calculate the y𝑦-intercept.6=3(9)+b6=3(9)+𝑏Step 4: Solve for the y𝑦-intercept (b𝑏). Perform the multiplication on the right side of the equation to clear the parenthesis.6=6= +b+𝑏Next, subtract 2727 from both sides of the equation and simplify to solve for b𝑏. =b=𝑏Step 5: Rewrite original equation in Step 1. Fill in the value for b𝑏 into the slope-intercept form of the equation and simplify.y=3x+b𝑦=3𝑥+𝑏y=𝑦= x−𝑥− The equation in slope-intercept form is y=3x−21𝑦=3𝑥−21.

To find an equation for a line between two points, you need two things.The y𝑦-intercept of the graph.The slope of the line.Previously, you learned how to determine the slope between two points. The slope between any two points (x1,y1)(𝑥1,𝑦1) and (x2,y2)(𝑥2,𝑦2) is: m=y2−y1x2−x1𝑚=𝑦2−𝑦1𝑥2−𝑥1.The procedure for determining a line given two points is the same five-step process as writing an equation given the slope and a point. First, name the points as being the first point and the second point,(x1,y1)(𝑥1,𝑦1) (x2,y2)(𝑥2,𝑦2)(−2,6)(−2,6) (4,−6)(4,−6)Next, use the coordinates of these points to fill in the formula for calculating the slope of the line.m=y2−y1x2−y1=−6−64−(−2)=𝑚=𝑦2−𝑦1𝑥2−𝑦1=−6−64−(−2)=  −12−12=−2=−2The slope of the line is −2−2.Next, use the slope of the line and the coordinates of one point to calculate the y𝑦-intercept of the line.m=−2𝑚=−2 and (−2,6)(−2,6)Next, substitute the values into the slope-intercept form of an equation.y=mx+b𝑦=𝑚𝑥+𝑏 =−2(=−2( )+b)+𝑏Next, perform the multiplication to clear the parenthesis.6=4+b6=4+𝑏Next, subtract 44 from both sides of the equation to solve for b𝑏.6−4=4−4+b6−4=4−4+𝑏 =b=𝑏Then, substitute the values for m𝑚 and b𝑏 into the slope-intercept form of the equation of a line.y=mx+b𝑦=𝑚𝑥+𝑏y=𝑦= x+𝑥+

A straight line can be represented by an equation of the form y = mx + b where, m is the slope and b is the intercept. The intercept b represents:

The pair of equations x = a and y = b graphically represents lines whichare

A straight line can be represented by an equation of the form y = mx + b where, m is the slope and b is the intercept. The intercept b represents:Group of answer choicesthe value of x for y = 0a value which is inverse of the slopethe value of y for x = 0a constant that depends on the nature of the instrument to be usedamount of change in y for a unit change in x