Answer:
See graph below of the line y - 5 = - 4 (x - 3) OR y = -4 x + 17
Explanation:
We can write the equation for such a line using the point-slope form [(y - y₁) = m (x - x₁)] where m = - 4 & (x₁ , y₁) = ( 3, 5 ). We can then find the x and y-intercept. The line we draw through these three points will be the line we are trying to find.
Equation of the Line
y - 5 = - 4 (x - 3)
Finding x and y-intercepts
y-intercept is 'c' when the line is in the slope-intercept form (y = mx + c)
since y - 5 = - 4 (x - 3)
y - 5 = -4 x + 12
y = -4 x + 17
∴ point of the y-intercept is (0, 17)
x-intercept occurs when y = 0
y = -4 x + 17
0 = -4 x + 17
-17 = -4x
x = ¹⁷/₄
∴ point of the x-intercept is (¹⁷/₄, 0)
Graph the line
We can now plug in the points and draw the line.
See the example below.
Note: You only need two points to graph the line. I just did a third as a check.