In the 𝑥𝑦-plane, the slope of line 𝑙 passing through point 𝐴 with coordinates (3,6) is –3. Quantity A Quantity B The 𝑥-intercept of line 𝑙
Question
In the 𝑥𝑦-plane, the slope of line 𝑙 passing through point 𝐴 with coordinates (3,6) is –3. Quantity A Quantity B The 𝑥-intercept of line 𝑙
Solution
The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept.
Given that the line l passes through the point A(3,6) and has a slope of -3, we can substitute these values into the equation to find the y-intercept (b).
6 = -3*3 + b 6 = -9 + b b = 6 + 9 b = 15
So, the equation of the line l is y = -3x + 15.
The x-intercept of a line is the value of x when y = 0. We can find this by setting y = 0 in the equation of the line and solving for x.
0 = -3x + 15 3x = 15 x = 15 / 3 x = 5
So, the x-intercept of line l is 5.
Similar Questions
In the 𝑥𝑦-plane, line 𝑙 with slope 3 passes through the points 𝐴 and 𝐵. If the coordinates of point 𝐴 are (2,10), which of the following can be the coordinates of point 𝐵?
A line has a slope of 6 and passes through the point (–3,–18). Write its equation in slope-intercept form.
A line has a slope of 1 and a y-intercept of –6. Write its equation in slope-intercept form.
A line passes through the points (–2,6) and (1,–9). Write its equation in slope-intercept form.
Write the point-slope form of the line that passes through (6, 1) and is perpendicular to a line with a slope of -3. Include all of your work in your final answer. Type your answer in the box provided to submit your solution.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.