Question

Write the slope-intercept form of the equation of the line through the given point with the given slope.

(0, 1), m = -6
(5, 5), m = 75

Answer 1

To write the slope-intercept form of the equation of a line, we use the formula y = mx + b, where m is the slope and b is the y-intercept. For the given points and slopes, substitute the values into the formula and solve for the y-intercept. The equations of the lines are y = -6x + 1 and y = 75x - 370.

Step-by-step explanation:

To write the slope-intercept form of the equation of a line, we use the formula y = mx + b, where m is the slope and b is the y-intercept.

For the point (0, 1) and slope -6, we have y = -6x + b. Substituting the coordinates of the point, we get 1 = -6(0) + b. Solving for b, we find b = 1.

So the equation of the line is y = -6x + 1.

Similarly, for the point (5, 5) and slope 75, we have y = 75x + b. Substituting the coordinates of the point, we get 5 = 75(5) + b. Solving for b, we find b = -370.

Thus, the equation of the line is y = 75x - 370.