Question

1. write an equation in slope intercept form for a line with a slope of 2 and a y-intercept of
2. write an equation in standard form for a line with a slope of $\frac{-2}{5}$ and a y-intercept of -1.
3. write an equation in point-slope form for a line with a slope of 2 that passes through (3, -1).
4. write an equation in slope-intercept form for a line that contains the point $\left(\frac{1}{4},2\

ight)$ and has a slope of 0.

Explanation:

Problem 3:

Step1: Recall slope - intercept form

The slope - intercept form of a line is given by the formula \(y=mx + b\), where \(m\) is the slope of the line and \(b\) is the \(y\) - intercept.

Step2: Substitute the values of \(m\) and \(b\)

We are given that the slope \(m = 2\) and the \(y\) - intercept \(b\) (assuming the missing value for \(y\) - intercept is a typo, but if we assume the intended \(y\) - intercept is, say, let's assume the original problem might have a number, but since it's a bit unclear, but if we take a general case, if the \(y\) - intercept is \(b\), then the equation is \(y = 2x + b\). But if we assume the \(y\) - intercept was supposed to be a number, for example, if it was \(3\) (maybe a typo), then \(y=2x + 3\). But since the original problem's \(y\) - intercept part is a bit unclear (the image shows a partial number), but following the formula, if slope \(m = 2\) and let's say the \(y\) - intercept \(b\) (if it was a number like \(3\)), then \(y=2x + 3\).

Problem 11:

Step1: Recall slope - intercept form

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. Given \(m=-\frac{2}{5}\) and \(b=- 1\), so the equation in slope - intercept form is \(y=-\frac{2}{5}x-1\).

Step2: Convert to standard form

The standard form of a line is \(Ax + By=C\), where \(A\), \(B\), and \(C\) are integers and \(A\geq0\).
Start with \(y =-\frac{2}{5}x-1\). Multiply both sides of the equation by \(5\) to get rid of the fraction: \(5y=-2x - 5\).
Then, add \(2x\) to both sides of the equation: \(2x+5y=-5\).

Problem 12:

Step1: Recall point - slope form

The point - slope form of a line is given by \(y - y_1=m(x - x_1)\), where \(m\) is the slope of the line and \((x_1,y_1)\) is a point on the line.

Step2: Substitute the values

We are given that \(m = 2\) and the point \((x_1,y_1)=(3,-1)\). Substitute these values into the point - slope formula: \(y-(-1)=2(x - 3)\), which simplifies to \(y + 1=2(x - 3)\), which matches the given answer.

Problem 13:

Answer:

\(y = 2x+3\) (depends on the actual \(y\) - intercept value, but following the formula)

Problem 11