Writing Equations in Slope Intercept Form

Front

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

Back

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you identify the slope from the equation y = mx + b?

Back

The slope (m) is the coefficient of x in the equation.

Front

What does the y-intercept represent in the equation y = mx + b?

Back

The y-intercept (b) represents the point where the line crosses the y-axis.

Front

How can you convert the standard form of a linear equation to slope-intercept form?

Back

To convert from standard form Ax + By = C to slope-intercept form, solve for y to isolate it on one side of the equation.

Front

What is the slope of the line represented by the equation y = -2x + 4?

Back

The slope of the line is -2.

Front

If a line has a slope of 1/2, what does this indicate about the line's steepness?

Back

A slope of 1/2 indicates that for every 2 units moved horizontally, the line moves up 1 unit, making it a gentle incline.

Front

How do you graph the equation y = 3x + 6?

Back

To graph y = 3x + 6, start at the y-intercept (0, 6) and use the slope (3) to find another point by going up 3 units and right 1 unit.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the rate of change of y with respect to x; it shows how steep the line is and the direction it goes.

Front

How do you determine the equation of a line given a slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant from left to right.