Find The Slope-Intercept Form Of The Line Equation ✓ Solved

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m

Determine the equation of a line in slope-intercept form (y = mx + b) that passes through a specific point with a given slope. This involves calculating the y-intercept (b) using the point-slope form of a line and then rewriting it in slope-intercept form. The task includes sketching the line as well.

For example, if the point is (x1, y1) and the slope is m, the equation can be found by substituting into y - y1 = m(x - x1) to find the y-intercept and then expressing y as a function of x.

Sample Paper For Above instruction

The problem requires constructing the equation of a straight line in slope-intercept form that passes through a given point and has a specified slope. To demonstrate the process, consider a representative example: suppose the point is (2, 3) and the slope m is 4. Using the point-slope form, we write:

y - 3 = 4(x - 2)

Expanding this, we get:

y - 3 = 4x - 8

Adding 3 to both sides gives the slope-intercept form:

y = 4x - 5

This is the desired equation of the line in slope-intercept form. The y-intercept here is at (0, -5). To sketch the line, plot the point (2, 3) and mark the y-intercept at (0, -5). Draw the line passing through these points, noting that for every unit increase in x, y increases by 4 units due to the slope.

In applying this process to the specific examples in the assignment, take the given point coordinates and the slope m, substitute into the point-slope form, and simplify to find the slope-intercept form. Additionally, sketch the lines on a coordinate plane to visualize their position and inclination. This approach applies universally to all line equations with given points and slopes, enabling students to understand the relationship between point-slope form and slope-intercept form effectively.

Overall, mastering this skill is essential for graphing linear functions, interpreting slope as rate of change, and understanding the geometric representation of linear equations in coordinate geometry.

References

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