Graph the line with the slope of -4 and passing through ( 3, 5 ).

Step-by-step 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.

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step-by-step explanation: