Front

What is the point-slope form of a linear equation?

Back

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

Front

How do you convert a linear equation from slope-intercept form to point-slope form?

Back

To convert from slope-intercept form (y = mx + b) to point-slope form, identify a point (x_1, y_1) on the line and use the slope m in the point-slope formula.

Front

Given the point (4, -7) and slope m = -1/4, write the equation in point-slope form.

Back

y + 7 = -1/4(x - 4)

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

If a line has a slope of -3, what does this indicate about the line's direction?

Back

A slope of -3 indicates that the line is decreasing; for every 1 unit increase in x, y decreases by 3 units.

Front

Write the equation of the line in point-slope form that goes through the point (10,5) and has a slope of -3.

Back

y - 5 = -3(x - 10)

Front

What is the significance of the point (5, -1) in the equation y + 1 = -3(x - 5)?

Back

The point (5, -1) is a point on the line represented by the equation, confirming that the equation is valid.

Front

How do you find the slope between two points, (-7, 0) and (1, 8)?

Back

The slope m is calculated using the formula m = (y_2 - y_1) / (x_2 - x_1). For these points, m = (8 - 0) / (1 - (-7)) = 8/8 = 1.

Front

What is the x-intercept of a line?

Back

The x-intercept is the point where the line crosses the x-axis, which occurs when y = 0.

Front

Given the equation y = 5x + 2, what is the slope?

Back

The slope of the line is 5.