Answer:
10.0
Step-by-step explanation:
see attached for reference.
given two points in the x-y axis (x₁, y₁) and (x₂, y₂)
the distance bettween them is given by
Distance, D = √ ( (x₂-x₁)² + (y₂-y₁)² )
In our case we are given points (9,10) and (-1,9)
substituting these into the formula , we get:
D = √ ( (9-10)² + (-1-9)² )
= √ ( (-1)² + (-10)² )
= √ ( 1 + 100 )
=√101
= 10.04988
= 10.0 (rounded to nearest tenth)
The value of c, if a line with a slope of 3/4 that passes through the points (1,8) and (5,c), is 11.
<h3>What is the equation of a line?</h3>A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
Given that the line has a slope of 3/4 and passes through the point (1,8). Therefore, we need to substitute the slope and the coordinates in the equation of the line, to get the value of the y-intercept.
y = mx + c
8 = (3/4)(1) + c
8 = (3/4) + c
c = 8 - (3/4)
c = 29/4
Now, the line also passes through (5,c), therefore, if we substitute the value of slope and y-intercept in the equation,
y = mx + c
c = (3/4)(5) + (29/4)
c = (15/4) + (29/4)
c = 44/4
c = 11
Hence, the value of c, if a line with a slope of 3/4 that passes through the points (1,8) and (5,c), is 11.
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