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Question

An illustration shows a coordinate plane with four quadrants. The x-axis ranges from negative 50 to 50 in ten unit increments. The y-axis ranges from negative 20 to 120 in ten unit increments. An upward slanting line is graphed on the coordinate plane. The line passes through two plotted points. The points have coordinates at left parenthesis 10 comma 70 right parenthesis and left parenthesis 25 comma 100 right parenthesis.

Write the equation of the linear function shown on the graph.

(1 point)
Responses

y=12x−25
y equals Start Fraction 1 over 2 End Fraction x minus 25

y=2x+50
y equals 2 x plus 50

y=2x−25
y equals 2 x minus 25

y=12x+50
y equals Start Fraction 1 over 2 End Fraction x plus 50
Remaining Attempts : 3
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Answer 1

To find the equation of the line passing through the points (10, 70) and (25, 100), we can first calculate the slope (m) using the formula:

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

Let \( (x_1, y_1) = (10, 70) \) and \( (x_2, y_2) = (25, 100) \).

Calculating the slope:

\[ m = \frac{100 - 70}{25 - 10} = \frac{30}{15} = 2 \]

Now that we have the slope \( m = 2 \), we can use the point-slope form of the line equation:

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

Using the point (10, 70):

\[ y - 70 = 2(x - 10) \]

Now, simplify this:

\[ y - 70 = 2x - 20 \] \[ y = 2x - 20 + 70 \] \[ y = 2x + 50 \]

Thus, the equation of the line is:

\[ y = 2x + 50 \]

The correct response is:

y = 2x + 50