Give the coordinates of a point on the line whose equation in point-slope form is 

*y* − (−2) = 1/4(*x* − 5).




The given equation is in point-slope form:

\[
y - (-2) = \frac{1}{4}(x - 5)
\]

We can simplify this to:

\[
y + 2 = \frac{1}{4}(x - 5)
\]

To find a point on this line, let's pick an \(x\)-value, substitute it into the equation, and solve for \(y\). 

Let’s choose \(x = 5\) (since the point-slope form is based on this value). Substituting \(x = 5\) into the equation:

\[
y + 2 = \frac{1}{4}(5 - 5)
\]

\[
y + 2 = \frac{1}{4}(0) = 0
\]

\[
y = -2
\]

So, one point on the line is \((5, -2)\).

Would you like further clarification or more details on this?

Here are 5 related questions:
1. How do you convert point-slope form to slope-intercept form?
2. What is the slope of the line from the given equation?
3. How do you find the slope between two points on a line?
4. What other points could lie on this line?
5. How do you determine if a point lies on a given line?

**Tip**: In point-slope form, the point \((x_1, y_1)\) is given directly by the numbers inside the parentheses!

Give the coordinates of a point on the line whose equation in point-slope form is y − (−2) = 1/4(x − 5).

Discover how to find the coordinates of a point on a line given the point-slope form equation y + 2 = 1/4(x - 5). Learn about key algebraic concepts including the point-slope form, slope calculation, and properties of linear equations. Suitable for students in Grades 8-10.

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