How to Find the Equation of a Line with Slope and Point

TL;DR

To find the equation of a line given a slope of 7 and the point (-4, -11), use the slope-intercept form, y = mx + b. Substitute the point into the equation to solve for b, resulting in the full equation y = 7x + 17.

Transcript

A line has a slope of 7 and goes through the point negative 4, negative 11. What is the equation of this line in slope-intercept form? So the equation of any line in slope-intercept form is y is equal to mx plus b, where m is the slope and b is the y-intercept. Now, in this problem right here, they tell us the slope. They tell us that a line has a ... Read More

Key Insights

• 🫥 The equation of a line can be determined when the slope and one point on the line are given.
• 😃 Slope-intercept form (y = mx + b) is commonly used to write the equation of a line.
• 🥘 Substituting the coordinates of a point into the equation allows us to find the y-intercept of the line.
• 🫥 The slope of a line represents how steep the line is and can be used to determine the direction of the line on a graph.

Questions & Answers

Q: What is the equation of the line in slope-intercept form?

The equation of the line in slope-intercept form is y = 7x + 17. This means the slope is 7, and the y-intercept is 17.

Q: How do we find the y-intercept of the line?

To find the y-intercept, we substitute the coordinates of a given point on the line (-4, -11) into the equation y = 7x + b. By solving for b, we find that the y-intercept is 17.

Q: What is the significance of the slope of 7?

The slope of 7 indicates that for every unit increase in the x-coordinate, the y-coordinate increases by 7 units. It represents a steep upward-sloping line.

Q: How would the line be graphed?

The line passes through the point (0, 17), which is the y-intercept. When x increases by 1, y increases by 7. Therefore, the line would start at (0, 17) and move upward with a steep slope of 7.

Summary & Key Takeaways

• The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

• The given line has a slope of 7, so the equation will be y = 7x + b.

• To find the y-intercept, we can substitute the coordinates (-4, -11) into the equation and solve for b.

• The equation of the line is y = 7x + 17.