Questions: Homework 11 Question 7, 6.1.39 HW Score: 37.5%, 6 of 16 Part 1 of 3 Points: 0 of 1 Save (a) Find the equation of the straight line through (3,4) and (5,6). (b) Find the equation of the line through (-5,5) with slope 6. (c) Find a point that lies on both of the lines in (a) and (b). a. Find the equation of the straight line through (3,4) and (5,6). (Type an equation.)

Solution Steps

To find the equation of a straight line through two points, we can use the point-slope form of a line equation. First, calculate the slope using the formula \((y_2 - y_1) / (x_2 - x_1)\). Then, use one of the points and the slope to write the equation in the form \(y - y_1 = m(x - x_1)\), where \(m\) is the slope.

To find the slope \( m \) of the line passing through the points \( (3, 4) \) and \( (5, 6) \), we use the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 4}{5 - 3} = \frac{2}{2} = 1.0 \]

Using the point-slope form of the line equation \( y - y_1 = m(x - x_1) \), we can rearrange it to find the y-intercept \( b \):

\[ b = y_1 - m \cdot x_1 = 4 - 1.0 \cdot 3 = 4 - 3 = 1.0 \]

Now that we have the slope and the y-intercept, we can write the equation of the line in slope-intercept form \( y = mx + b \):

\[ y = 1.0x + 1.0 \]

Final Answer