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.

We are given both the slope and y𝑦-intercept so writing the equation in slope-intercept form is a breeze! Label both the slope and y𝑦-intercept and them substitute them into the general form of slope-intercept form.m=𝑚= b=𝑏= So, y=4x−3𝑦=4𝑥−3.We now have our slope-intercept form of the line.

Write the equation of the line in slope-intercept form (y = mx + b).Slope = Point on the line = (, )

Point-slope form requires that we have the slope and a point on the line. Recall that the y𝑦-intercept is where the graph crosses the y𝑦-axis and we can write it as a coordinate point. The y𝑦-intercept of this equation is −3−3 so the coordinate point would be:(( ,, ))We now have the slope and a point on the line so we can write an equation in point-slope form.y−3=4(x−0)

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, )).

Now, let’s use the graph to write the equation in point-slope form this time.To write an equation in point-slope form, we need the slope and one point on the line. We already know the slope so let’s state that again so we don’t forget.m=12𝑚=12We just need one point on the graph (usually we pick a different point than the y𝑦-intercept). We used two points to find the slope so let’s just pick one of those. We will use the point (2,−1)(2,−1). We have the slope and a point so now let’s plug it into point-slope form.y−y1=m(x−x1)𝑦−𝑦1=𝑚(𝑥−𝑥1)y−(−1)=𝑦−(−1)=  (x−(𝑥− ))y+1=12(x−2)𝑦+1=12(𝑥−2)