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The equation of a line is 8x-4y=40

What is the equation in slope-intercept form

3 answers

To convert the equation of the line \(8x - 4y = 40\) into slope-intercept form, we need to solve for \(y\) in terms of \(x\). The slope-intercept form is given by:

\[ y = mx + b \]

where \(m\) is the slope and \(b\) is the y-intercept.

Starting with the original equation:

  1. Move \(8x\) to the right side:

\[ -4y = -8x + 40 \]

  1. Divide every term by \(-4\) to solve for \(y\):

\[ y = 2x - 10 \]

Thus, the equation in slope-intercept form is:

\[ y = 2x - 10 \]

Here, the slope \(m\) is \(2\), and the y-intercept \(b\) is \(-10\).

What is the slope and what is the y-intercept?

From the slope-intercept form of the equation \(y = 2x - 10\):

  • The slope (m) is \(2\).
  • The y-intercept (b) is \(-10\).

This means that for every 1 unit increase in \(x\), \(y\) increases by 2 units, and the line crosses the y-axis at the point \((0, -10)\).