Question

Find an equation of the line satisfying the conditions. Write your answer in the slope-intercept form. Passes through \((2,4)\) and \((3,8)\)

Short answer

The equation of the line in slope-intercept form that passes through the points (2,4) and (3,8) is \(y = 4x - 4\).

Step-by-step solution

Find the slope (m)

To find the slope (m) of the line, we can use the formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \) Using the given points (2,4) and (3,8), we have: \[ m = \frac{8 - 4}{3 - 2} = \frac{4}{1} = 4 \]

Find the y-intercept (b)

We now use the slope-intercept form (y = mx + b) and one of the given points to solve for the y-intercept (b). Let's use the point (2,4): \[ 4 = 4 \cdot 2 + b \] Solve for b: \[ b = 4 - 8 = -4 \]

Write the equation of the line

Now that we have the slope and y-intercept, we can write the equation of the line in slope-intercept form: \[ y = 4x - 4 \] This is the equation of the line that passes through the points (2,4) and (3,8) in slope-intercept form.