Answer:
y=2x-6
Step-by-step explanation:
The line has an x-intercept of (3,0) and crosses through the point (5,4). Using these points, we can find the slope using the slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}= \frac{4-0}{5-3} =\frac{4}{2}=2[/tex]
To write the equation of the line, substitute m=2 and the point (5,4) into the [tex]y-y_1 = m(x-x_1)[/tex].
[tex]y-4=2(x-5)\\y-4=2x-10\\y=2x-6[/tex]
Answer: The required equation of the line is [tex]y=2x-6.[/tex]
Step-by-step explanation: We are give to write the equation of a straight line with x-intercept 3 and passing through the point (5, 4).
Since the given line has x-intercept 3, so it will pass through the point (3, 0).
The slope of a line passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
Since the given line passes through the points (3, 0) and (5, 4), so its slope will be
[tex]m=\dfrac{4-0}{5-3}=\dfrac{4}{2}=2.[/tex]
Therefore, the equation of the line is given by
[tex]y-0=m(x-3)\\\\\Rightarrow y=2(x-3)\\\\\Rightarrow y=2x-6.[/tex]
Thus, the required equation of the line is [tex]y=2x-6.[/tex]
