Question

Write an equation for the graph shown in the form $\boxed{y = \phantom{blahhhhhh}}$. [asy] unitsize(0.4 cm); pair A, B, C, D, E, F, G, H, I, J; int i; A = (1,1.2); B = (5,2); C = (-5,0); for (i = -10; i <= 10; ++i) { draw((i,-10)--(i,10),gray(0.7)); draw((-10,i)--(10,i),gray(0.7)); } draw((-10,0)--(10,0),linewidth(1.5*bp),Arrows(6)); draw((0,-10)--(0,10),linewidth(1.5*bp),Arrows(6)); draw((-10,-1)--(10,3),red); label("$x$", (10,0), NE); label("$y$", (0,10), NE); dot("$(1,1.2)$", A, N); dot("$(5,2)$", B, SE); dot("$(-5,0)$", C, NW); [/asy]

Answer 1

The equation for the red line is:
`\[ \boxed{y = 0.2x + 1} \]`

The equation for the red line can be determined using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

Let's find the slope m using the given points
`\((1,1.2)\) and \((5,2)\):`

`\[ m = \frac{\text{change in } y}{\text{change in } x} = (2 - 1.2)/(5 - 1) = (0.8)/(4) = 0.2 \]`

Now that we have the slope, we can use either point to find the y-intercept (\(b\)):

`\[ 1.2 = 0.2(1) + b \]`

`\[ b = 1 \]`

Therefore, the equation for the red line is:
`\[ \boxed{y = 0.2x + 1} \]`

Complete question:

Write an equation for the graph shown in the form y.