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Versions of Linear Equations Quick Check
2 of 52 of 5 Items
Question
A line passes through the points (8,10)
and (13,17)
. What is the equation of the line in point-slope form?(1 point)
Responses

y−10=7/5(x−8)
y minus 10 equals Start Fraction 7 over 5 End Fraction left parenthesis x minus 8 right parenthesis

y+17=7/5(x+13)
y plus 17 equals Start Fraction 7 over 5 End Fraction left parenthesis x plus 13 right parenthesis

y−10=5/7(x−13)
y minus 10 equals Start Fraction 5 over 7 End Fraction left parenthesis x minus 13 right parenthesis

y−10=5/7(x−8)

1 answer

To find the equation of the line in point-slope form that passes through the points \( (8, 10) \) and \( (13, 17) \), we first need to calculate the slope of the line.

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting in our points \( (8, 10) \) and \( (13, 17) \):

\[ m = \frac{17 - 10}{13 - 8} = \frac{7}{5} \]

Now that we have the slope, we can use the point-slope form equation, which is:

\[ y - y_1 = m(x - x_1) \]

We can use either point. Let's use the point \( (8, 10) \):

\[ y - 10 = \frac{7}{5}(x - 8) \]

Thus, the equation of the line in point-slope form is:

\[ y - 10 = \frac{7}{5}(x - 8) \]

Looking at the response options provided, the correct answer is:

y − 10 = 7/5(x − 8).