Write an equation of each line described below. Write the lines in slope-intercept form, y

To write the equation of a line in slope-intercept form $y = mx + b$, we need the slope $m$ and the y-intercept $b$. If we are given a point $P(x_1, y_1)$ that lies on the line and the slope $m$, we can use the point-slope form of the equation and then convert it to slope-intercept form.

A) The line that passes through the point $P(0, -5)$ and has a slope of $\frac{1}{10}$.

Since the line passes through $(0, -5)$, this point is the y-intercept. Therefore, $b = -5$. The slope is given as $m = \frac{1}{10}$.

So, the equation is: $y = \frac{1}{10}x - 5$

B) The line that passes through the point $P(2, 1)$ and has a slope of $7$.

We use the point-slope form of the line equation: $y - y_1 = m(x - x_1)$ Substituting $(x_1, y_1) = (2, 1)$ and $m = 7$: $y - 1 = 7(x - 2)$

Distribute and simplify to get the slope-intercept form: $y - 1 = 7x - 14$ $y = 7x - 13$

Final Answers:

A) $y = \frac{1}{10}x - 5$

B) $y = 7x - 13$

Would you like any details or further clarification on these solutions?

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Here are some related questions you might find interesting:

1. What is the slope-intercept form for a horizontal line passing through a given point?
2. How do you find the equation of a line if you are given two points?
3. What is the significance of the y-intercept in a linear equation?
4. How do you convert from slope-intercept form to standard form?
5. How do you determine if two lines are parallel based on their equations?

Tip: Always double-check that the y-intercept corresponds to the point where the line crosses the y-axis when writing equations in slope-intercept form.