Determining the Equation of a Line with Given Slope and Y-Intercept

The equation of a line in slope-intercept form is a fundamental concept in algebra. The slope-intercept form of the equation of a line is given by:

y mx b

where m is the slope and b is the y-intercept. The y-intercept is the value of y when x is zero.

Given the slope m 3 and the y-intercept b -4, we substitute these values into the slope-intercept form equation:

y 3x - 4

So, the equation of the line is:

y 3x - 4

This means that for any given value of x, the corresponding value of y can be found using the equation y 3x - 4.

Explanation

The slope-intercept form of the equation of a line is y mx b. Given that the slope m is 3 and the y-intercept b is -4, the equation of the line is:

y 3x - 4

Graphical Representation

The graph of the line y 3x - 4 is a straight line that passes through the y-axis at the point (0, -4) and has a slope of 3. This means that for every one unit increase in x, y increases by 3 units.

Solution

Given the slope m 3 and the y-intercept b -4, we can write the equation of the line as:

y 3x - 4

This is the equation of the line in slope-intercept form. The graphical representation of this line is shown below: