Question

Write an equation of the line shown. Then use the equation to find the value of x when y = 26

Answer 1

First find slope
(y2-y1)/(x2-x2)
Use points (1,2) and (-1,-6)
(-6-2)/(-1-1) = -8/-2 = 4
Slope int equation: y = mx + b
m = slope, b = y intercept
Plug in what we know (use any point)
2 = 4(1) + b
2 = 4 + b, b = -2
Equation: y = 4x - 2
Plug in y = 26
26 = 4x - 2
28 = 4x, x = 7
Solution: x = 7

Answer 2

y = 4x - 2

When y = 26, x = 7.

Explanation:

Use the two points on the line to calculate the slope of the line, then use this slope and the y-intercept to write an equation for the line.

Slope formula:

• (y2 - y1)/(x2 - x1)

We have these two points on the graph: (1, 2), (-1, -6).

Substitute these points into the slope formula and find the slope of the line.

• (-6-2)/(-1-1)
• (-8)/(-2)
• 4

The slope of the line is 4. Now, use the point-slope formula to write an equation for the line.

Point-slope formula:

• y - y1 = m(x - x1)
• y - 2 = 4(x - 1)
• y -2 = 4x - 4
• y = 4x - 2

To find the value of x when y = 26, substitute y = 26 into the equation and solve for x.

• 26 = 4x - 2
• 28 = 4x
• x = 7