Question

Graph paper graph align with the Y intercept zero, -4 in the X intercept three, zero find the equation of the line

Answer 1

To find the equation of the line given the y-intercept (0, -4) and the x-intercept (3, 0), we can use the point-slope form of the equation, which is
`\(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\)` is a point on the line, and m is the slope.

First, calculate the slope
`(\(m\))`:

`\[ m = \frac{{\text{{change in }} y}}{{\text{{change in }} x}} \]`

`\[ m = \frac{{0 - (-4)}}{{3 - 0}} = (4)/(3) \]`

Now, choose one of the points (let's use the y-intercept, (0, -4)) and substitute into the point-slope form:

`\[ y - (-4) = (4)/(3)(x - 0) \]`

Simplify:

`\[ y + 4 = (4)/(3)x \]`

Finally, rearrange to slope-intercept form
`(\(y = mx + b\))`:

`\[ y = (4)/(3)x - 4 \]`

So, the equation of the line is
`\(y = (4)/(3)x - 4\)`.