The points(0,2) and (4,-10) lie on the same line and the points (-5,-3) and (2,11) lie on another line.

question:

write equations in slope-intercept form of these two lines

y = -3x + 2 and y = 2x + 7

Step-by-step explanation:

Here you're asked to perform the same calculations twice.

Case I:

"The points (0,2) and (4,-10) lie on the same line."  Thus, the slope of this line is m = rise / run = (-10 - 2) / (4 - 0), or m = -12/4, or m = -3.

Then the equation of this line, obtained from the point-slope form, is y = mx +b, or (using the point (0, 2) ):

2 = -3(0) + b.  Thus, b = 2 and the desired equation is   y = -3x + 2.

Case II:

"The points (-5, -3) and (2, 11) lie on another line."

Thus, the slope is m = rise / run = (11 - [-3]) / (2 - [-5]), or m = 14/7, or m = 2.

Let's use this m = 2, the point (2, 11) and the slope-intercept equation to determine the line through  (-5, -3) and (2, 11):

11 = 2(2) + b, so that b = 7.  The desired equation is thus  y = 2x + 7.

i hope this is what you were looking for.

see attached graph

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step-by-step explanation: