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Answer:
m=5 and b=-10
Step-by-step explanation:
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The slope of line (m) is 5 and y-intercept of the line at y= -10
What is the slope of the line?
The slope of a line (m) is the measure of the steepness and the direction of the line .
Formula of slope of line
[tex]m = \frac{Change\\\ in\\\ value\\\ of\\\ y }{Change\\\ in\\\ value\\\ of\\\ x} = \frac{(y2-y1) }{(x2-x1)}[/tex]
The coordinates of the first point represent x1 and y1.
The coordinates of the second points are x2, y2.
What is intercepts?
The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
What is the equation of line passing through point?
The point form of a line passing through these points is:
[tex]y - y1 = m (x - x1)[/tex]
where,(x,y) are variables
(x1,y1) are points given
According to question,
A line passes through the points [tex](3,5)[/tex] and [tex](2,0).[/tex]
Where, Slope of line (m) [tex]=\frac{5-0}{3-2}[/tex]
m [tex]=5[/tex]
Now, Equation of line passing through the point [tex](3,5)[/tex] is
[tex]y - y1 = m (x - x1)[/tex]
(x1,y1) = (3,5)
substituting the values on equation
[tex](y-5)=5(x-3)[/tex]
y -5 = 5x - 15
y = 5x - 10 --------------------- (1)
Now, y- intercept is :
where a line crosses the y-axis or x = 0
At [tex]x=0[/tex] ,
Substituting value in equation (1)
y = 5*0 - 10
y = -10
So, [tex]y-[/tex]intercept [tex]=-10[/tex]
Hence, The slope of line (m) is 5 and y-intercept of the line at y= -10
Learn more about slope and intercepts here:
https://brainly.com/question/3605446?referrer=searchResults
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