Find the slope and y-intercept for the following equation by writing it in the form 𝑦=𝑚𝑥+𝑏. Then, graph the equation.-5𝑥-6𝑦=30Equation:
Question
Find the slope and y-intercept for the following equation by writing it in the form 𝑦=𝑚𝑥+𝑏. Then, graph the equation.-5𝑥-6𝑦=30Equation:
Solution
First, let's rewrite the equation -5x - 6y = 30 in the form y = mx + b.
Step 1: Add 5x to both sides of the equation to isolate the y term on one side:
-5x + 5x - 6y = 30 + 5x This simplifies to: -6y = 5x + 30
Step 2: Divide every term by -6 to solve for y:
y = -5/6x - 5
So, the slope (m) of the line is -5/6 and the y-intercept (b) is -5.
To graph the equation, you would:
- Start by plotting the y-intercept (0, -5) on the graph.
- From there, use the slope to find the next point. The slope is -5/6, which means for every 6 units you move to the right (positive x direction), you move 5 units down (negative y direction). So, from the y-intercept, you would move 6 units to the right and 5 units down and plot that point.
- Draw a line through the two points to complete the graph.
Similar Questions
Graph the line with slope 34 and y-intercept −9.
ProblemGraph the function y=−3x+5𝑦=−3𝑥+5. SolutionTo graph the function without making a table, follow these steps:Identify the y𝑦-intercept: b=𝑏= Plot the intercept: (0,(0, ))Identify the slope: m=𝑚= (This is equal to −31−31, so the rise is −3−3 and the run is 11.)Move over 11 unit and down 33 units to find another point on the line: (1,2)(1,2).Draw the line through the points (0,5)(0,5) and (1,2)(1,2).
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.
Write an equation in slope-intercept form for the line with y-intercept 6 and slope −15.
If y varies directly with x, Write an equation relating x and y when y = -30 and x = 6.Group of answer choices-6x = -30yy = 5xy = -5x6x = -30y
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