Find the equation of the line with slope 2/3 and intercept on the y-axis is 5:
Answers
Answer:
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Step-by-step explanation:
Some useful information about lines
Fact
You can use this fact when you know:
Slope formula:
two points on a line
Slope-intercept formula: y = mx + b
the slope and y-intercept of a line
Point-slope formula: y - y1 = m(x - x1)
the slope of a line and a point on the line
Parallel lines have equal slopes
the slope of a line
The slopes of perpendicular lines are opposite reciprocals
the slope of a line
The most difficult part of working with points, slopes and lines is determining which formula to use when solving specific problems. When you are trying to solve a problem, ask yourself these questions:
What am I supposed to find?
What do I already know?
What method will I use?
The chart below outlines the methods that are appropriate to use when solving specific types of problems.
What do you want to find?
What do you know already?
Method to use
Slope of a line Coordinates of two points on the line Use the slope formula
Slope and y-intercept of a line Equation of a line in standard form Write the equation in slope-intercept form
Equation of a line Slope of the line and a point on that line Use the point-slope formula
Equation of a line Slope and y-intercept of a line Use the slope-intercept formula
Equation of a line Coordinates of two points on the line Use the slope formula to find the slope of the line, then use the slope and one of the points in the point-slope formula
Equation of a line parallel to a given line Equation of the given parallel line and a point on your line Write the equation of the given line in slope-intercept form to determine its slope, then use that same slope and your point in the point-slope formula
Equation of a line perpendicular to a given line Equation of the given perpendicular line and a point on your line Write the equation of the given line in slope-intercept form to determine its slope, then use the opposite reciprocal of that slope and your point in the point-slope formula
Let's look at some examples.
Example 1 What is the slope of a line through the points (2,3) and (4,-5) ?
What do we want to find? The slope of a line
What do we already know? Two points on the line
What method will we use? Use the slope formula
Example 2 What are the slope and y-intercept of 2x - 3y = 5 ?
What do we want to find? The slope and y-intercept
What do we already know? The equation of a line in standard form
What method will we use? Write the equation in slope-intercept form
2x - 3y = 5
- 3y = - 2x + 5
y = 2/3 x - 5/3
Since the equation now is in y = mx + b form, we can identify the slope m=2/3 and the y-intercept b=-5/3
Example 3 What is the equation of a line with slope - 2 which passes through (3,-5)?
What do we want to find? The equation of a line
What do we already know? The slope and a point on the line
What method will we use? Use the point-slope formula
m = -2, (x1, y1) = (3, -5)
y - y1 = m(x - x1)
y - -5 = -2(x - 3)
y + 5 = -2x + 6
y = -2x + 1
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Answer:
Find the equation of the line with slope 2/3 and intercept on the y-axis is 5:
Step-by-step explanation:
the formula forline
y=mx+c
given that m=2/3 and c=5
equation of line
y=(2/3)x+5