Question

What is the equation of the following line written in slope-intercept form?
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Answer 1

`y = 5x`

Explanation:

Line equation is given as y = mx + b

Where, m is the slope of the line, which is,

`m = (y2 - y1)/(x2 - x1)`

b is the y-intercept. It is the point at which the line crosses the y-axis for which the value of x = 0.

=>Find m and b to derive an equation for the line.

using the 2 coordinate pairs, (1, 5), (-1, -5),

Let, x2 = -1,

x1 = 1,

y2 = -5,

y1 = 5

`m = (y2 - y1)/(x2 - x1)`

`m = (-5 - 5)/(-1 - 1)`

`m = (-10)/(-2)`

`m = 5`

From the graph given, the line intercepts the y-axis at point 0. Therefore b = 0.

Plug in the values of m and b in the line of equation.

y = mx + b

y = 5x + 0

y = 5x

Therefore, the equation of the line, in the graph above, written in slope-intercept form is:

`y = 5x`