Question

Write an equation in slope-intercept form, of the line that passes through (0, 3) and (−5, 2.5).

Answer 1

The slope-intercept form:

$y=mx+b\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

m - slope, b - y-intercept

We have the points (0, 3) - y-intercept (b = 3) and (-5, 2.5). Substitute:

$m=\dfrac{2.5-3}{-5-0}=\dfrac{-0.5}{-5}=\dfrac{5}{50}=\dfrac{5:5}{50:5}=\dfrac{1}{10}=0.1$

Answer: y = 0.1x + 3.

Answer 2

The equation of a line, in slope-intercept form, that passes through points (0, 3) and (-5, 2.5) is: $\mathbf{y = 0.1x + 3}$

Recall:

• Slope-intercept form equation for a straight line is: y = mx + b
• b is the y-intercept
• m is the slope

Given the two points a line passes through as:

(0, 3) and (−5, 2.5)

Find the slope (m) using: $\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1} }$

• Let,

$(0, 3) = (x_1, y_1)\\\\(-5, 2.5) = (x_2, y_2)$

• Substitute

$Slope (m) = \frac{2.5 - 3}{-5 - 0} = \frac{-0.5}{-5}\\\\\mathbf{Slope (m) = 0.1}$

Find the y-intercept (b) by substituting (x, y) = (0, 3) and m = 0.1 into y = mx + b and solve for b

• Thus:

$3 = 0.1(0) + b\\\\3 = 0 + b\\\\3 = b\\\\\mathbf{b = 3}$

Write the equation by substituting m = 0.1 and b = 3 into y = mcx + b:

$\mathbf{y = 0.1x + 3}$

Therefore, the equation of a line, in slope-intercept form, that passes through points (0, 3) and (-5, 2.5) is: $\mathbf{y = 0.1x + 3}$

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