Question

Can Someone show me how to get these 3 answers step by step.
1. Write the equation of a line in slope intercept form that passes through (2, 4) and (5, 4).

2. Write an equation of a line in slope intercept form that is parallel to y = 3x+6 and passes through the point (-10, 2.5)

3.Write an equation of a line in slope intercept form that is perpendicular to y = -4x -2 and passes through the point (-16, -11).

Answer 1

1) The slope intercept form of a line is y = mx + b
where m is the slope, and b is the y-intercept. You have 2 coordinates (2, 4) and (5, 4) which you could label as \((x_1, y_1)\) and \((x_2,y_2)\). Then the slope is calculated as \[ slope = m=\frac{y_2-y_1}{x_2-x_1}\]

Once you find the slope m, you can plug in any point [(2, 4) or (5,4)] into the x and y positions in your line equation, and then solve for b to get the y-intercept

Answer 2

For 2) You just need to realize that if the line is parallel, then both lines have the same slope, but the intercept will be different. So you already know the slope of the line you need need find, so you just plug in (-10. 2.5) into "x" and "y" in your line equation as you did in #1)

For 3) When 2 lines are perpendicular, the product of the 2 slopes is equal to -1. So, if the slope of one line is \(m_1\) and the slope of the second line is \(m_2\), then:
\(m_1 \times m_2 =-1\)
So you can determine was is \(m_2\) based on that equation above , since you know \(m_1\).