Question

Use point-slope or slope-intercept form to match the equations in slope-intercept form with the given slope "m" and point (s, y).

m = 3, point (4, 5)
m = 3, point (-2, 1)
m = 3, point (1, -3)

Answer 1

The slope-intercept form for the given slope, m, and points are y = 3x - 7 for the point (4,5), y = 3x + 7 for the point (-2, 1), and y = 3x - 6 for the point (1, -3).

Step-by-step explanation:

To find the linear equations in slope-intercept form with a given slope, m, and a point, (s, y), we use the formula y = mx + b, where m is the slope and b is the y-intercept. Since the slope, m, is given as 3 for all points, we just need to solve for b using the given points.

For the point (4,5), we substitute m = 3 and the coordinates into the formula to get 5 = 3(4) + b. Solving for b, we find that b = -7. Therefore, the equation is y = 3x - 7.

The same process applies to the point (-2, 1). Substituting into the formula gives us 1 = 3(-2) + b, yielding b = 7. Thus, the equation for this point is y = 3x + 7.

Finally, for the point (1, -3), plugging in the values gives us -3 = 3(1) + b. Solving for b gives b = -6, making the equation y = 3x - 6.