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The equation of a line is given below.

-3x + 4y = – 12
Find the slope and the y-intercept and then use them to graph the line of the equation on the grid

The equation of a line is given below. -3x + 4y = – 12 Find the slope and the y-intercept-example-1

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Answer:

  • slope: 3/4
  • y-intercept: -3

Explanation:

To put the equation in slope-intercept form, solve for y.

-3x +4y = -12

4y = 3x -12 . . . . . . add 3x

y = 3/4x -3 . . . . . . divide by 4

This tells you the slope (coefficient of x) is 3/4, and the y-intercept is -3.

Points you can plot using this knowledge are ...

(0, -3) . . . . y-intercept

(4, 0) . . . . . x the first non-zero multiple of 4; makes the x-term an integer

The line will go through these two points.

_____

Additional comment

The given equation is in the form ...

ax +by = c

In this form, the intercepts are easily found by setting the other term to zero.

x-intercept: x = c/a . . . . = -12/-3 = 4

y-intercept: y = c/b . . . . = -12/4 = -3

When the intercepts are integers, it can be easier to draw the line through them, than to mess with the slope calculation.

The equation of a line is given below. -3x + 4y = – 12 Find the slope and the y-intercept-example-1
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