Question

Find the coordinates of the points of intersection of the graphs with coordinate axes: y= -1/4x+2

Answer 1

x-intercept: (8, 0)

y-intercept: (0, 2)

Explanation:

Given equation:

`y=-(1)/(4)x+2`

The graph intersects the y-axis when x = 0.

To find the graph's y-intercept, substitute x = 0 into the equation and solve for y:

`\begin{aligned}x=0 \implies y&=-(1)/(4)(0)+2\\y&=0+2\\y&=2\end{aligned}`

Therefore, the coordinates of the point of intersection with the y-axis are:

• (0, 2)

The graph intersects the x-axis when y = 0.

To find the graph's x-intercept, substitute y = 0 into the equation and solve for x:

`\begin{aligned}y=0\implies \-(1)/(4)x+2&=0\\-(1)/(4)x&=-2\\x&=8\end{aligned}`

Therefore, the coordinates of the point of intersection with the x-axis are:

• (8, 0)

Answer 2

Solutions below.

Explanation:

This question is asking us to find the points of intersection, which means its asking to find the x-intercept abd y-intercept.

To find the x-intercept, we know that y = 0.

Therefore we can substitute y = 0 into the line equation:

`0 = - (1)/(4) x + 2 \\ - (1)/(4) x = - 2 \\ x = - 2 / - (1)/(4) \\ = 2 * 4 \\ = 8`

Therefore the point of the x-intercept is (8,0).

Likewise to find the y-intercept, we know x = 0.

Therefore we can substitute x = 0 into the line equation:

`y = - (1)/(4) (0) + 2 \\ = 0 + 2 \\ = 2`

Therefore the point of the y-intercept is (0,2).