Question

Write an equation of the line in slope-intercept form from the given points on the graph:

(0,5) (3,4)

Answer 1

To find the equation of the line in slope-intercept form, we first need to find the slope of the line.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

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

Using the points (0, 5) and (3, 4), we can calculate the slope:

m = (4 - 5)/(3 - 0)
m = -1/3

Now that we have the slope, we can use the point-slope form of a linear equation to write the equation of the line:

y - y1 = m(x - x1)

Using the point (0, 5), we can rewrite the equation as:

y - 5 = (-1/3)(x - 0)

Simplifying further, we have:

y - 5 = (-1/3)x

To convert this equation to slope-intercept form (y = mx + b), we need to isolate y on the left-hand side:

y = (-1/3)x + 5

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

y = (-1/3)x + 5